It is interesting to note that the scale dividing the ultra and infra long-wavelength limits coincides with the so-called decoupling limit, where we can neglect the perturbations in the metric and may only consider those in the matter sector. That is, the gravitational background is considered to be completely classical, and the Goldstone boson picture for the curvature perturbation becomes manifest [1]}
– only the scalar field is quantum mechanical in the classical gravitational background.
Interestingly, in such a limit the equation of state of 2EMT is
\(w \approx -1/3\)  in all gauge choices we examine in this section.
